Some complexity results for polynomial rational expressions

Authors:
P.-C. Héam
Affiliations:
Laboratoire d'Informatique et d'Algorithmique, Fondements et Applications, Université Paris 7, caes 7014, 2 place Jussieu, F-75251, Paris Cedex 05, France
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

It is known that any languages of level 3/2 of the Straubing-Thérien hierarchy can be written as a polynomial expression, that is, a finite union of languages of the form A0*B1A*1 ... B*kAk where the Ai and Bi are subsets of the alphabet. In this paper we prove that such a polynomial expression for a 3/2-level language can be of exponential size. More precisely we exhibit an n-state minimal automaton recognizing a level 3/2 language for which the shortest polynomial expresion has exponential size in n.